The behavior of the correlation function \(c(r)\)  in the limit of \(r \rightarrow 0\)  is generally an interesting question, which provides information on the nature of the scattering contrast (see the discussion by Ciccariello, Goodisman, and Brumberger [1]}). When sharp interfaces in a sample separate homogeneous regions with a uniform (constant) scattering length density, then the correlation function exhibits a finite slope at the origin (compare Eqs. (REF ) and (REF ) for uniformly magnetized nanoparticles). This is the content of the well-known Porod law, which predicts a characteristic asymptotic \(q^{-4}\)  dependency of the SANS cross section [2]}. By contrast, structures with a nonuniform scattering length density profile, such as the smoothly varying magnetization profiles \(\mathbf {M}(\mathbf {r})\)  of micromagnetics, are characterized by a \(c(r)\)  that exhibits a zero slope at \(r=0\)  and concomitant steeper power-law exponents of the SANS cross section [3]}. In the present case, we are dealing with a system with a potentially nonuniform magnetization on one side of the interface (inside the particle) and a zero magnetization on the other side of the interface. The behavior of \(c(r)\)  at small distances also depends on the spin distribution in the vicinity of the surface and, therefore, on the surface anisotropy and the related boundary conditions for the magnetization. This question deserves a separate consideration and is beyond the scope of the present paper.
